How to Solve Factorisation — Step by Step Guide

Factorise algebraic expressions using common factors, grouping and identities. This guide covers Class 8 to 8.

Step-by-Step Method

  1. 1

    Look for a common factor in all terms and take it out.

  2. 2

    If no common factor, try grouping terms in pairs and factor each pair.

  3. 3

    Use algebraic identities: a² - b² = (a+b)(a-b), a² + 2ab + b² = (a+b)², a² - 2ab + b² = (a-b)².

  4. 4

    For quadratic expressions ax² + bx + c: split the middle term into two terms that multiply to give ac and add to give b.

  5. 5

    Always verify by expanding the factors back.

Worked Example

Problem: Factorise x² - 9.

Solution: This is a² - b² = (a+b)(a-b). So x² - 9 = (x+3)(x-3).

Common Mistakes to Avoid

  • ✗

    Not taking out the highest common factor first.

  • ✗

    Incorrectly identifying the identity to use.

  • ✗

    Sign errors when splitting the middle term.

  • ✗

    Leaving the factorisation incomplete.

Practice Factorisation on SparkEd

Get free chapter-wise practice questions aligned to your board:

CBSE Class 8 Factorisation

Master Factorisation with Free Practice

30,000+ questions, AI solver for instant help, and printable worksheets. 100% free.

Start Practising FreePlay Zone (Class 1-5)

Frequently Asked Questions

How do I solve Factorisation problems?
Look for a common factor in all terms and take it out. If no common factor, try grouping terms in pairs and factor each pair.
What are common mistakes in Factorisation?
Not taking out the highest common factor first. Incorrectly identifying the identity to use.
Which class covers Factorisation?
Factorisation is typically taught in Class 8. SparkEd has free practice for all these grades.
Where can I practise Factorisation for free?
SparkEd offers free chapter-wise practice for Factorisation aligned to CBSE, ICSE, and IB curricula. Visit sparkedmaths.com to start.

SparkEd Maths — sparked.coms@gmail.com — www.sparkedmaths.com